A comparison of mip-based decomposition techniques and VNS approaches for batch scheduling problems

Authors:
Andreas Klemmt;Gerald Weigert;Christian Almeder;Lars Mönch
Affiliations:
Technische Universität Dresden, Dresden, Germany;Technische Universität Dresden, Dresden, Germany;University of Vienna, Vienna, Austria;University of Hagen, Hagen, Germany
Venue:
Winter Simulation Conference
Year:
2009

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Abstract

This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication facilities. With respect to some practical motivated process constraints, like equipment dedication and unequal batch-sizes, we model the problem as unrelated parallel batch machines problem with incompatible job families and unequal ready times of the jobs. Our objective is to minimize the total weighted tardiness (TWT) of the jobs. Given that the problem is NP-hard, we propose two different solution approaches. The first approach works with a time window-based mixed integer programming (MIP) decomposition. The second approach uses a variable neighbourhood search (VNS). Using randomly generated test instances, we show that the proposed algorithms outperform common dispatching rules that cannot deal with the given constraints effectively.